Tests of the Martingale Hyf’othesis for Foreign Currency Futures with Time-varying Volatility

The martingale hypothesis for daily and weekly rates of change of futures prices for five currencies is tested in this paper. With daily data, we find some evidence against the null hypothesis for each currency. Although institutionally imposed limits on daily price changes were binding fairly often in the earlier years of the sample, the results are not substantially different when data affected by limit moves are removed. Trading day effects in foreign currency futures and spot prices introduce complicated day of the week patterns in futures price. For this reason, we retest the martingale hypothesis with weekly data and reject the null hypothesis for only one currency. For this currency, one interpretation of the evidence is that a time-varying risk premium exists.